In 1926, the Third Coinage of George V was introduced on many denominations including pennies.
Additionally, a Fourth Coinage was introduced in 1927, and a new "small head" design was introduced on pennies and halfpennies from 1928.
The obverse and reverse designs of George V remained unchanged, except for minor modifications, from its introduction in 1911 to 1925.
The Second Coinage only affected the silver coins, the silver content of which was reduced from 92.5% to 50%.

"Ghosting"
Most coins are only singly struck whereas medals are often double struck. Because coins need to be produced economically and quickly in large quantities to meet demand, they usually receive only one single blow from the dies. The metal momentarily melts and flows under the high pressure and raised temperature, so that metal flows into the "cut out" areas of the die which become the raised part of the coin. If the amounts of metal displaced into the obverse and reverse designs are not approximately equal, the flow of metal may not be completed, leaving weakly struck areas on one, sometimes both, sides of the coin. Also it is necessary for the designer to be aware of the effects of matching raised and depressed areas of design on corresponding areas of the opposite sides of the coin.
Because the portrait used on early George V coins featured a large head in quite high relief, there was more metal displaced into the obverse than into the reverse. This often resulted in a "shadow" or "ghost" of the head design showing on the reverse, and also a general weakness of the reverse design, particularly noticeable on the pennies.

Solving The Ghosting Problem - New Bronze Alloy
Ghosting had affected the larger coins of Edward VII and of George V. Experiments were started about 1920 to eliminate or reduce this design problem.
One experiment was to alter the bronze alloy, so that between 1920 and 1922, some bronze coins were produced using an alloy of:-

Metal

Percentage

Copper

95.5

Tin

3.0

Zinc

1.5

No pennies were minted from 1923 to 1925, but the new alloy was used for all bronze coins from 1923 onwards.
The reduced tin content produced a softer alloy, which allowed the metal to flow more easily on striking, and therefore reduce the ghosting effect, and at the same time reduce die wear and breakage.

Solving The Ghosting Problem - New Obverse Designs
Clearly the introduction of the new alloy did not completely solve the ghosting problem, as Sir Bertram Mackennal, the designer of the portrait on the coins of George V, attempted to solve the problem by producing a new obverse design known as the "modified effigy". This was introduced on the halfpennies in 1925, and on the halfcrown, shilling, sixpence, threepence, penny, and farthing in 1926.

Giving Up The Ghost
The modified effigy design still did not completely eliminate the ghosting problem, and in 1928, a new smaller head was introduced on the bronze coins, and was retained successfully until the end of George's reign in 1936.

The Modified Effigy
The modified effigy appears to have been a complete re-sculpturing of the obverse design. All the hairlines are different, the overall relief may be slightly lower, the truncation at the neck is less pronounced, and the engravers initials are further to the right.
According to Peck*, other design differences include:-
There are no stops after the designer's initials (BM) on the modified head.
The beard and mustache have been retouched.
The two dots of each colon are set farther apart.
Effectively, the modified effigy is a new portrait of the same person by the same sculptor, and as such is considerably different. In practice, however, many people find great difficulty in perceiving the differences. As often, the solution is to look not only for the major differences, but to look at the overall design and learn to appreciate the entirely different "look" of the design. A trick taught to me in school art lessons was to half close the eyes, and this trick works in many situations; I do not fully understand how this works, if there is anybody out there who can provide an explanation, I would be delighted to hear to from them.

Photographs
We show on this page a photograph of a non-modified 1926 penny, and also one of a 1927 penny, which features the modified effigy. Unfortunately, the coins are not in the same condition, when we next obtain a near mint condition 1926, we will replace the photograph. It would help when making comparisons to have two coins in similar grades, but our photos do clearly show most of the redesigned features.
As the coins wear, the wear patterns are different on the two designs, due to differences in the location of the high spots on each design.
We have also provide larger versions of the photos, each 640 x 480, so those interested can see the differences in more detail.

* An excellent book, "English Copper, Tin and Bronze Coins in the British Museum 1558 - 1958", by C. Wilson Peck, published by the Trustees of the British Museum in 1964, is useful for information on this and other designs. It was originally priced at £5.12s.6d (=£5.625), but is now out of print. I have been told that second-hand copies change hands at about £100 in good condition.